As representative solution algorithms for mathematical programming problems, linear programming, mixed-integer linear programming, integer programming, quadratic programming, non-linear programming and so on are known. Linear programming is a solution algorithm for a mathematical programming problem wherein decision variables are continuous variables, and any constraints and an objective function are expressed as linear expressions (linear programming problem). Mixed-integer linear programming is a solution algorithm for a mathematical programming problem wherein decision variables are continuous variables and discrete variables, and any constraints and an objective function are expressed as linear expressions (mixed-integer linear programming problem). Integer programming is a solution algorithm for a mathematical programming problem wherein decision variables are expressed by discrete variables (integer programming problem). Quadratic programming is a solution algorithm for a mathematical programming problem wherein an objective function is expressed as a quadratic expression and constraints are expressed as linear expressions (quadratic programming problem). Non-linear programming is a solution algorithm for a mathematical programming problem wherein any constraints and an objective function are expressed as arbitrary continuous functions that are not linear (non-linear programming problem). When a mathematical plan to be derived is describable as any one of the above typical mathematical programming problems, it can be solved by using a general solver that is appropriate to each existent mathematical programming problem.
As a problem similar to the operation plan problem for storage tanks for storing liquefied natural gas, for example, a “method for controlling reception facility” disclosed in the following Patent Literature 1 is known. This conventional art provides a method for controlling a reception facility capable of planning an operation procedure that allows rapid response to unscheduled reception or discharge while keeping desired material properties as much as possible and minimizes the energy cost, in a short time even when the reception facility is enlarged and complicated, for example, due to increase in numbers of tanks, and assumes fluids such as petroleum, naphtha or gas as the material to be stored.